The invention described in this disclosure is an apparatus and method for clamping semiconductor wafers or other substrates or workpieces during etching, CVD, or surface modification processes. The purpose of the invention is to achieve improved heat transfer during processing between the wafer/substrate and a temperature controlled pedestal used for supporting it in the process chamber. The typical level of process heat put into the wafer during plasma-based etching or deposition processes will be up to about 10 Watts per centimeter squared while the maximum acceptable temperature differential between wafer/substrate and pedestal is less than about 100 Celsius. In such low gas pressure environments typical for plasma-based processes, the heat removal from the wafer/substrate by gaseous conduction may be inadequate to meet requirements. This invention achieves excellent heat transfer to the pedestal from the wafer/substrate when there is a thin, resilient, electrically insulating layer (tape) bonded to the wafer/substrate or the pedestal. Wafer/substrate clamping for improved process heat removal is achieved by a combination of vacuum clamping of the wafer/substrate beginning prior to evacuation of the processing chamber, along with or followed by electrostatic clamping of the wafer/substrate which continues during processing. The invention also permits the wafer/substrate to be rapidly and safely released from the electrostatic clamping when the chamber is returned to atmospheric pressure by a providing a slight pressure increase, above atmospheric pressure, between wafer and pedestal. The pedestal may have some roughening or narrow grooves on the wafer clamping surface, and some small holes from its surface leading to an evacuated plenum or channel within the pedestal. Alternatively, the pedestal may have a layer of a porous metal extending from its surface down to the evacuated channel or plenum which permits gas to be evacuated. These structures allow vacuum pumping of gas that might otherwise be trapped between the insulating layer and the pedestal. When a wafer/substrate is placed on the pedestal by loading at atmospheric pressure, vacuum pumping through the pedestal is commenced. This causes the workpiece to be pressed to the pedestal clamping surface with approximately atmospheric pressure compressing the soft layer against its clamping surface. This provides sufficient contact of the soft layer with the pedestal to greatly improve heat transfer from the wafer/substrate to the pedestal. A voltage is applied to the pedestal, beginning any time after the wafer is on the pedestal, to further clamp the wafer electrostatically. As the processing chamber is then pumped down to operating pressure for processing the electrostatic clamping voltage maintains sufficient pressure of the wafer/substrate against the pedestal to maintain the heat conductive contact between the soft layer and the pedestal. This permits good heat conduction to be maintained during the low pressure plasma-based etching or CVD processing. Following processing when the wafer/substrate is to be removed it may be rapidly de-clamped from the electrostatic clamping by application of a slight over-atmospheric pressure in the reservoir or pumping channels within the pedestal.